A novel synchrosqueezing transform associated with linear canonical transform

Synchrosqueezing transforms have aroused great attention for its ability in time-frequency energy rearranging and signal reconstruction, which are post-processing techniques of the time-frequency distribution. However, the time-frequency distributions, such as short-time Fourier transform and short-time fractional Fourier transform, cannot change the shape of the time-frequency distribution. The linear canonical transform (LCT) can simultaneously rotate and scale the time-frequency distribution, which enlarges the distance between different signal components with proper parameters. In this study, a convolution-type short-time LCT is proposed to present the time-frequency distribution of a signal, from which the signal reconstruction formula is given. Its resolutions in time and LCT domains are demonstrated, which helps to select suitable window functions. A fast implementation algorithm for the short-time LCT is provided. Further, the synchrosqueezing LCT (SLCT) transform is designed by performing synchrosqueezing technique on the short-time LCT. The SLCT inherits many properties of the LCT, and the signal reconstruction formula is obtained from the SLCT. Adaptive selections of the parameter matrix of LCT and the length of the window function are introduced, thereby enabling proper compress direction and resolution of the signal. Finally, numerical experiments are presented to verify the efficiency of the SLCT.